How Do You Calculate the Distance Between Two Stars in a Binary System?

[kraigandrews]

Homework Statement

2 stars are separated by a distancce r, one star has mass 2/3M the other has mass 2M (M is a solar mass). The period of revolution is 5 years, calculate r.

Homework Equations

Fg=(GM1M2)/r^2

The Attempt at a Solution

Ok so I know that the binary star system revolves around its center of mass point, however I am unsure how to find it, Xcm=(M1X1+M2X2)/(M1+M2) but how is it found without knowing X1 and X2

 

[tiny-tim]

hi kraigandrews!

(try using the X² and X₂ icons just above the Reply box )

2 stars are separated by a distancce r, one star has mass 2/3M the other has mass 2M (M is a solar mass). The period of revolution is 5 years, calculate r.
…
… Xcm=(M1X1+M2X2)/(M1+M2) but how is it found without knowing X1 and X2

X X₁ and X₂ are all measured from the same point …

you choose the point (for example, you can chooose one of the stars)

 

[kraigandrews]

so just checking to make sure but my cm point then is:
(M1X)/(M1+M2)

 

[tiny-tim]

so just checking to make sure but my cm point then is:
(M1X)/(M1+M2)

yes

 

[kraigandrews]

thanks!